Linear Inequalities

Concept:Translate machine time limits into linear inequalities for production variables.Explanation:Let $x$ = number of units of product $A$, $y$ = number of units of product $B$.Machine 1: maximum 60 hours. $A$ needs 2 hours, $B$ needs 1 hour. So $2x + y \leq 60$.Machine 2: maximum 40 hours. $A$ needs 1 hour, $B$ needs 2 hours. So $x + 2y \leq 40$.Also $x \geq 0$, $y \geq 0$ (non‑negative production).Answer:The required inequalities are $2x + y \leq 60$ and $x + 2y \leq 40$.This matches option C (with the understanding that the second inequality is $\leq 40$).